Francois/Fransway

I am looking for a connection for my Fransway relatives and those with the surname Francois or Lefrancois. My great-grandmother was Grace Angelette Fransway. She was born in about 1860. Her father was Lewis Fransway. They lived in New York City in the 1800's. I think that Grace had a younger sister named Mary. Grace married William Adams.

There was an earlier Lewis Fransway who served in the War of 1812 in New Jersey. He was in Capt. Peter Souder's company, Infantry, which was in Lieut-Col. Joshua Howell's Regiment. He may have been the latter Lewis Fransway's father.

I have heard that the Fransways were French and that the original name may have come from Francois or Lefrancois. It has been suggested that the East coast Fransways may have previously been in Maine and perhaps in Canada before that.